Question

unit 1 section 12 assignment - geometry

1. what is the sum of the measures of the interior angles of a pentagon (5 - gon)?
2. the sum of the interior angles of a polygon is 1080°. how many sides does it have? number of sides: 8
3. find the measure of a single interior angle of a regular dodecagon (12 - gon).
4. five of the interior angles of a hexagon measure 110°, 120°, 130°, 140°, and 150°. what is the measure of the sixth interior angle? sixth interior angle = ______

Explanation:

Step1: Recall interior - angle sum formula

The sum of the interior angles of a polygon is given by the formula $S = 180(n - 2)$, where $n$ is the number of sides of the polygon.

Step2: Solve for pentagon

For a pentagon, $n = 5$. Substitute $n = 5$ into the formula: $S=180\times(5 - 2)=180\times3 = 540$.

Step3: Solve for polygon with sum 1080

We know $S = 180(n - 2)=1080$. Divide both sides by 180: $n - 2=\frac{1080}{180}=6$. Then add 2 to both sides: $n=6 + 2=8$.

Step4: Solve for dodecagon interior - angle

For a dodecagon, $n = 12$. First, find the sum of the interior angles: $S = 180\times(12 - 2)=180\times10 = 1800$. Since it is a regular dodecagon, each interior angle $\theta=\frac{1800}{12}=150$.

Step5: Solve for hexagon's sixth angle

For a hexagon, $n = 6$. The sum of the interior angles $S=180\times(6 - 2)=180\times4 = 720$. The sum of the five given angles is $110+120+130+140+150 = 650$. The sixth angle is $720-650 = 70$.

Answer:

1. $540$
2. $8$
3. $150$
4. $70$